Legal claims defining the scope of protection, as filed with the USPTO.
1. A complex multiplier providing a complex product of a first complex input, includes a first component input collection comprising an A 1 R and an A 1 I, and a second complex number defined by a LogA 2 R and an LogA 2 I, comprising: a collection of logarithm calculators, receiving said first complex input to create a first complex log version number; a collection of adders, adding said first complex log version number to said LogA 2 R to create a LogA 1 RA 2 R and a LogA 1 IA 2 R while adding said first complex log version number to said LogA 2 I to create a LogA 1 IA 2 I and a LogA 1 RA 2 I; a collection of exponential calculators, exponentiating each member of a complex log component collection to create a corresponding member of a complex numeric component collection; and wherein said complex log component collection includes said LogA 1 RA 2 R and said LogA 1 IA 2 I, said LogA 1 IA 2 R and said LogA 1 RA 2 I; wherein said complex numeric component collection includes an A 1 RA 2 R, an A 1 IA 2 I, an A 1 IA 2 R, and an A 1 RA 2 I; wherein said complex product includes an A 12 R and an A 12 I; wherein said first complex log version number includes a LogA 1 R and a LogA 1 I; wherein whenever said A 1 R equals zero, said A 1 RA 2 R equals said zero and said A 1 RA 2 I equals said zero, further comprising: wherein whenever said A 1 R equals zero, said LogA 1 R indicates negative infinity; wherein whenever said LogA 1 R indicates said negative infinity, said LogA 1 RA 2 R indicates said negative infinity and said LogA 1 RA 2 I indicates said negative infinity; wherein whenever said LogA 1 RA 2 R indicates said negative infinity, said A 1 RA 2 R equals zero; and wherein whenever said LogA 1 RA 2 I indicates said negative infinity, said A 1 RA 2 I equals zero; wherein whenever said A 1 I equals said zero, said A 1 IA 2 R equals said zero and said A 1 IA 2 R equals said zero, further comprising: wherein whenever said A 1 I equals zero, said LogA 1 I indicates said negative infinity; wherein whenever said LogA 1 I indicates said negative infinity, said LogA 1 IA 2 R indicates said negative infinity and said LogA 1 IA 2 I indicates said negative infinity; wherein whenever said LogA 1 IA 2 R indicates said negative infinity, said A 1 IA 2 R equals zero; and wherein whenever said LogA 1 IA 2 I indicates said negative infinity, said A 1 IA 2 I equals zero.
2. The complex multiplier of claim 1 , further comprising: circuitry providing at least one member of a log-value collection; and wherein said log-value collection is comprised of said Log A 1 R, said Log A 1 I, said Log A 1 RA 2 R, said Log A 1 IA 2 I, said Log A 1 IA 2 R, and said Log A 1 RA 2 I.
3. The complex multiplier of claim 2 , wherein said circuitry providing said log-value collection member is comprised of at least one member of the collection comprising: circuitry providing said Log A 1 R; circuitry providing said Log A 1 I; circuitry providing said Log A 1 RA 2 R; circuitry providing said Log A 1 IA 21 ; circuitry providing said Log A 1 IA 2 R; and circuitry providing said Log A 1 RA 2 I.
4. The complex multiplier of claim 1 , further comprising at least one member of the collection comprising, for each of said complex numeric component collection members: circuitry providing said complex numeric component collection member.
5. The complex multiplier of claim 4 , further comprising: circuitry providing said complex numeric component collection member, for each of said complex numeric component collection members; circuitry providing said Log A 1 R; and circuitry providing said Log A 1 I.
6. An apparatus acting as an FFT radix engine for performing at least an FFT radix operation based upon said first complex input of claim 1 , comprising: said complex multiplier providing said complex product using said Log A 2 R and said Log A 2 I to define said second complex input; and said apparatus further comprising, for each of at least two current complex values, of: circuitry creating a previously presented complex value based upon said current complex value, a control for said current complex value, said complex input, and said complex product.
7. The apparatus of claim 6 , wherein said complex multiplier is further comprised of: circuitry providing at least one member of a log-value collection; wherein said log-value collection is comprised of said Log A 1 R, said Log A 1 I, said Log A 1 RA 2 R, said Log A 1 IA 2 I, said Log A 1 IA 2 R, and said Log A 1 RA 2 I; wherein said circuitry creating at least one of said previously presented complex values is further comprised of: means for creating at least a component of said current complex value based upon said current complex value, said control, said complex input, said complex product and said provided log-value collection member.
8. The apparatus of claim 6 , wherein said FFT radix operation includes at least an FFT Radix 2 operation.
9. The apparatus of claim 6 , wherein said FFT radix operation includes at least an FFT Radix 4 operation; and wherein said circuitry receiving said current complex values is further comprised of: said circuitry receiving at least four of said current complex values.
10. The apparatus of claim 6 , wherein said FFT radix operation includes at least an FFT Radix 8 operation; and said apparatus is further comprised of: circuitry calculating a second complex product based upon at least one member of the collection comprising said first complex input and said complex product; wherein said circuitry receiving said current complex values is further comprised of: said circuitry receiving at least eight of said current complex values; wherein for each of said current complex values, said circuitry creating said previously presented complex value is further comprised of: said circuitry creating said current complex value based upon said control, said complex input, and at least one member of the collection comprising said complex product and said second complex product.
11. The apparatus of claim 10 , wherein said circuitry calculating said second complex product is further comprised of at least one member of the collection comprising: circuitry calculating said second complex product as a multiple of said complex product; and a second of said complex multipliers providing said second complex product from said complex input.
12. The apparatus of claim 11 , wherein said circuitry calculating said second complex product as said multiple is comprised of a member of the collection comprising: said circuitry calculating a fixed multiple of said complex product to create said second complex product; and a third of said complex multipliers receiving said complex input as said complex product and said second complex input approximating said fixed multiple.
13. The apparatus of claim 6 , wherein said circuitry creating said previously presented complex value, is further comprised of: said circuit creating said previously presented complex value based upon said A 1 RA 2 R, said A 1 IA 2 I, said A 1 IA 2 R, and said A 1 RA 2 I.
14. The apparatus of claim 1 , further comprising a member of the collection comprising: a second of said logarithm calculator collections, receiving said second complex input to create said Log A 2 R and said Log A 2 I; and an input generator providing said Log A 2 R and said Log A 2 I.
15. The complex multiplier of claim 1 , wherein said exponential calculator collection is comprised of: a first member, calculating an exponentiation of an input as said Log A 1 RA 2 R to create said A 1 RA 2 R; a second member, calculating said exponentiation of said input as said Log A 1 IA 2 I to create said A 1 IA 2 I; a third member, calculating said exponentiation of said input as said Log A 1 IA 2 R to create said A 1 IA 2 R; and a fourth member, calculating said exponentiation of said input as said Log A 1 RA 2 I to create said A 1 RA 2 I.
16. The complex multiplier of claim 15 , wherein at least one of said exponential calculator collection members, is comprised of at least one member of an exponential calculator component collection comprising: a table, an arithmetic circuit fed by said table, a logic circuit operating upon an output of said arithmetic circuit to establish at least negation and zero for said exponentiation; wherein said table is implemented as at least one member of a collection comprising a memory, a combinatorial logic network, and a second combinatorial logic network feed by at least one members of the collection including said memory and said combinatorial logic network.
17. The complex multiplier of claim 15 , wherein at least one of said exponential calculator collection members, is further comprised of: said member, calculating said exponentiation of said input as a member of a non-log-value collection; wherein said non-log-value collection is comprised of the members of said complex numeric component, and the members of said first component input collection, said A 12 R, and said A 12 I.
18. The complex multiplier of claim 1 , wherein said collection of logarithm calculators, receiving said first complex input is further comprised of: a first member, calculating a logarithm of said A 1 R to create said Log A 1 R; and a second member, calculating a logarithm of said A 1 I to create said Log A 1 I.
19. The complex multiplier of claim 18 , wherein at least one of said logarithm calculator members is comprised of at least one member of a logarithm calculator component collection comprising: a logic circuit aligning said component input to access a table and drive an arithmetic circuit fed by said table; wherein said table is implemented as at least one member of a collection comprising a memory, a combinatorial logic network, and a second combinatorial logic network feed by at least one member of the collection including said memory and said combinatorial logic network.
20. The complex multiplier of claim 1 , further comprising: a second collection of adders, creating said complex product from said complex numeric component collection.
21. The complex multiplier of claim 20 , wherein said second adder collection, creating said complex product is further comprised of: a first member, subtracting said A 1 IA 2 I from said A 1 RA 2 R to create said A 12 R; and a second member, adding said A 1 IA 2 R to said A 1 RA 2 I to create said A 12 I.
22. The complex multiplier of claim 1 , wherein each member of said complex numeric component collection represents a floating point number.
23. An apparatus providing a complex product of a first complex input and a second complex number defined by a Log A 2 R and an Log A 2 I; wherein said first complex input includes a first component input collection comprising an A 1 R and an A 1 I; wherein said first complex log version number includes a Log A 1 R and a Log A 1 I; wherein said apparatus, comprising: means for receiving said first complex input to create a first complex log version number, further comprising: means for whenever said A 1 R equals zero, said Log A 1 R indicates negative infinity; and means for whenever said A 1 I equals zero, said Log A 1 I indicates negative infinity; means for adding said first complex log version number to said Log A 2 R of said second complex number to create a Log A 1 RA 2 R and a Log A 1 IA 2 I while adding said first complex log version number to said Log A 2 I of said second complex number to create a Log A 1 IA 2 R and a Log A 1 RA 2 I, further comprising: means for whenever said Log A 1 R indicates said negative infinity, said Log A 1 RA 2 R indicates said negative infinity and said Log A 1 RA 2 I indicates said negative infinity; and means for whenever said Log A 1 I indicates said negative infinity, said Log A 1 IA 2 R indicates said negative infinity and said Log A 1 IA 2 I indicates said negative infinity; means for exponentiating each of member of a complex log component collection to create a corresponding member of a complex numeric component collection including an A 1 RA 2 R, an A 1 IA 2 I, an A 1 IA 2 R, and an A 1 RA 2 I, comprising: means for whenever said Log A 1 RA 2 R indicates said negative infinity, said A 1 RA 2 R equals zero; means for whenever said Log A 1 RA 2 I indicates said negative infinity, said A 1 RA 2 I equals zero; means for whenever said Log A 1 IA 2 R indicates said negative infinity, said A 1 IA 2 R equals zero; and means for whenever said Log A 1 IA 2 I indicates said negative infinity, said A 1 IA 2 I equals zero; wherein said complex product includes an A 12 R and an A 12 I; wherein said A 12 R equals said A 1 RA 2 R minus said A 1 IA 2 I; and wherein said A 12 I equals said A 1 IA 2 R plus said A 1 RA 2 I.
24. The apparatus of claim 23 , further comprising: means for creating said complex product is further comprised of: means for subtracting said A 1 IA 2 I from said A 1 RA 2 R to create said A 12 R; and means for adding said A 1 IA 2 R to said A 1 RA 2 I to create said A 12 I.
25. The apparatus of claim 23 , wherein the means for receiving said first complex input is further comprised of: means for calculating a logarithm of said A 1 R to create said Log A 1 R; and means for calculating a logarithm of said A 1 I to create said Log A 1 I.
26. The apparatus of claim 25 , wherein at least one of the means for calculating said logarithm is comprised of at least one member of a logarithm calculator component collection comprising: a logic circuit aligning said component input to access a table and drive an arithmetic circuit fed by said table; wherein said table is implemented as at least one member of a collection comprising a memory, a combinatorial logic network, and a second combinatorial logic network feed by at least one member of the collection including said memory and said combinatorial logic network.
27. The apparatus of claim 25 , wherein the means for calculating said logarithm of said A 1 R to create said Log A 1 R, further comprises: means for whenever said A 1 R equals zero, said Log A 1 R indicates negative infinity; wherein the means for calculating said logarithm of said A 1 I to create said Log A 11 , further comprises: means for whenever said A 1 I equals zero, said Log A 1 I indicates negative infinity.
28. The apparatus of claim 23 , wherein the means for exponentiating is further comprised of: means for calculating an exponentiation of an input as said Log A 1 RA 2 R to create said A 1 RA 2 R; means for calculating said exponentiation of said input as said Log A 1 IA 2 I to create said A 1 IA 2 I; means for calculating said exponentiation of said input as said Log A 1 IA 2 R to create said A 1 IA 2 R; and means for calculating said exponentiation of said input as said Log A 1 RA 2 I to create said A 1 RA 2 I.
29. The apparatus of claim 28 , wherein at least one of the means for calculating said exponentiation is comprised of at least one member of an exponential calculator component collection comprising: a table, an arithmetic circuit fed by said table, a logic circuit operating upon an output of said arithmetic circuit to establish at least negation and zero for said exponentiation; wherein said table is implemented as at least one member of a collection comprising a memory, a combinatorial logic network, and a second combinatorial logic network fed by at least one member of the collection including said memory and said combinatorial logic network.
30. The apparatus of claim 28 , wherein at least one of the means for calculating said exponentiation is further comprised of: means for calculating said exponentiation of said input as a member of a non-log-value collection; wherein said non-log-value collection is comprised of the members of said complex numeric component, and the members of said first component input collection, said A 12 R, and said A 12 I.
31. The apparatus of claim 28 , wherein the means for calculating said exponentiation of said input as said Log A 1 RA 2 R to create said A 1 RA 2 R, further comprises: means for whenever said Log A 1 RA 2 R indicates said negative infinity, said A 1 RA 2 R equals zero; wherein the means for calculating said exponentiation of said input as said Log A 1 IA 2 I to create said A 1 IA 2 I, further comprises: means for whenever said Log A 1 IA 2 I indicates said negative infinity, said A 1 IA 2 I equals zero; wherein the means for calculating said exponentiation of said input as said Log A 1 IA 2 R to create said A 1 IA 2 R, further comprises: means for whenever said Log A 1 IA 2 R indicates said negative infinity, said A 1 IA 2 R equals zero; and wherein the means for calculating said exponentiation of said input as said Log A 1 RA 2 I to create said A 1 RA 2 I, further comprises: means for whenever said Log A 1 RA 2 I indicates said negative infinity, said A 1 RA 2 I equals zero.
32. The apparatus of claim 23 , further comprising: means for providing at least one member of a log-value collection; and wherein said log-value collection is comprised of said Log A 1 R, said Log A 1 I, said Log A 1 RA 2 R, said Log A 1 IA 2 I, said Log A 1 IA 2 R, and said Log A 1 RA 2 I.
33. The apparatus of claim 32 , wherein the means for providing said log-value collection member is comprised of at least one member of the collection comprising: means for providing said Log A 1 R; means for providing said Log A 1 I; means for providing said Log A 1 RA 2 R; means for providing said Log A 1 IA 2 I; means for providing said Log A 1 IA 2 R; and means for providing said Log A 1 RA 2 I.
34. The apparatus of claim 23 , further comprising at least one member of the collection comprising, for each of said complex numeric component collection members: means for providing said complex numeric component collection member.
35. The apparatus of claim 34 , further comprising: means for providing said complex numeric component collection member, for each of said complex numeric component collection members; means for providing said Log A 1 R; and means for providing said Log A 1 I.
36. An FFT radix engine for performing at least an FFT radix operation based upon said first complex input of claim 23 , comprising: the means of providing said complex product using said Log A 2 R and said imaginary plane-log-version to define said second complex input: means for receiving at least two current complex values; and, said apparatus further comprising, for each of said current complex values, of: means for receiving a control for said current complex value; and means for creating a previously presented complex value based upon said current complex value, said control, said complex input, and said complex product.
37. The apparatus of claim 36 , wherein said means providing said complex product is further comprised of: means for providing at least one member of a log-value collection; wherein said log-value collection is comprised of said Log A 1 R, said Log A 1 I, said Log A 1 RA 2 R, said Log A 1 IA 2 I, said Log A 1 IA 2 R, and said Log A 1 RA 2 I; wherein the means for creating at least one of said previously presented complex values is further comprised of: means for creating at least a component of said current complex value based upon said current complex value, said control, said complex input, said complex product and said provided log-value collection member.
38. The apparatus of claim 36 , wherein said FFT radix operation includes at least an FFT Radix 2 operation.
39. The apparatus of claim 36 , wherein said FFT radix operation includes at least an FFT Radix 4 operation; and wherein the means for receiving said current complex values is further comprised of: means for receiving at least four of said current complex values.
40. The apparatus of claim 36 , wherein said FFT radix operation includes at least an FFT Radix 8 operation; and said apparatus is further comprised of: means for calculating a second complex product based upon at least one member of the collection comprising said first complex input and said complex product; wherein the means for receiving said current complex values is further comprised of: means for receiving at least eight of said current complex values; wherein for each of said current complex values, the means for creating said previously presented complex value is further comprised of: means for creating said current complex value based upon said control, said complex input, and at least one member of the collection comprising said complex product and said second complex product.
41. The apparatus of claim 40 , wherein the means for calculating said second complex product is further comprised of at least one member of the collection comprising: means for calculating said second complex product as a multiple of said complex product; and a second of said means of claim 23 providing said second complex product from said complex input.
42. The apparatus of claim 41 , wherein the means for calculating said second complex product as said multiple is comprised of a member of the collection comprising: means for calculating a fixed multiple of said complex product to create said second complex product; and a third of said means of claim 23 receiving said complex input as said complex product and said second complex input approximating said fixed multiple.
43. The apparatus of claim 23 , further comprising a member of the collection comprising: a second of said means for receiving said second complex input to create said Log A 2 R and said Log A 2 I; and means for generating said Log A 2 R and said Log A 2 I.
Unknown
October 16, 2007
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